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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1408

Last change on this file since 1408 was 1360, checked in by hoffmann, 11 years ago
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[828]	1	MODULE lpm_collision_kernels_mod
[790]	2
[1036]	3	!--------------------------------------------------------------------------------!
	4	! This file is part of PALM.
	5	!
	6	! PALM is free software: you can redistribute it and/or modify it under the terms
	7	! of the GNU General Public License as published by the Free Software Foundation,
	8	! either version 3 of the License, or (at your option) any later version.
	9	!
	10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	13	!
	14	! You should have received a copy of the GNU General Public License along with
	15	! PALM. If not, see <http://www.gnu.org/licenses/>.
	16	!
[1310]	17	! Copyright 1997-2014 Leibniz Universitaet Hannover
[1036]	18	!--------------------------------------------------------------------------------!
	19	!
[790]	20	! Current revisions:
	21	! -----------------
[1347]	22	!
[1360]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_collision_kernels.f90 1360 2014-04-11 17:20:32Z raasch $
	27	!
[1360]	28	! 1359 2014-04-11 17:15:14Z hoffmann
	29	! New particle structure integrated.
	30	! Kind definition added to all floating point numbers.
	31	!
[1347]	32	! 1346 2014-03-27 13:18:20Z heinze
	33	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	34	! intrinsic function like MAX, MIN, SIGN
	35	!
[1323]	36	! 1322 2014-03-20 16:38:49Z raasch
	37	! REAL constants defined as wp_kind
	38	!
[1321]	39	! 1320 2014-03-20 08:40:49Z
[1320]	40	! ONLY-attribute added to USE-statements,
	41	! kind-parameters added to all INTEGER and REAL declaration statements,
	42	! kinds are defined in new module kinds,
	43	! revision history before 2012 removed,
	44	! comment fields (!:) to be used for variable explanations added to
	45	! all variable declaration statements
[1008]	46	!
[1093]	47	! 1092 2013-02-02 11:24:22Z raasch
	48	! unused variables removed
	49	!
[1072]	50	! 1071 2012-11-29 16:54:55Z franke
	51	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	52	!
[1037]	53	! 1036 2012-10-22 13:43:42Z raasch
	54	! code put under GPL (PALM 3.9)
	55	!
[1008]	56	! 1007 2012-09-19 14:30:36Z franke
[1007]	57	! converted all units to SI units and replaced some parameters by corresponding
	58	! PALM parameters
	59	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	60	! changed from 10. to 1.0
[829]	61	!
[850]	62	! 849 2012-03-15 10:35:09Z raasch
	63	! routine collision_efficiency_rogers added (moved from former advec_particles
	64	! to here)
	65	!
[836]	66	! 835 2012-02-22 11:21:19Z raasch $
	67	! Bugfix: array diss can be used only in case of Wang kernel
	68	!
[829]	69	! 828 2012-02-21 12:00:36Z raasch
[828]	70	! code has been completely reformatted, routine colker renamed
	71	! recalculate_kernel,
	72	! routine init_kernels added, radius is now communicated to the collision
	73	! routines by array radclass
[790]	74	!
[828]	75	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	76	!
[826]	77	! 825 2012-02-19 03:03:44Z raasch
	78	! routine renamed from wang_kernel to lpm_collision_kernels,
	79	! turbulence_effects on collision replaced by wang_kernel
	80	!
[791]	81	! 790 2011-11-29 03:11:20Z raasch
	82	! initial revision
[790]	83	!
	84	! Description:
	85	! ------------
[828]	86	! This module calculates collision efficiencies either due to pure gravitational
	87	! effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
	88	! including the effects of (SGS) turbulence (Wang kernel, see Wang and
	89	! Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8). The original code has been
	90	! provided by L.-P. Wang but is substantially reformatted and speed optimized
	91	! here.
	92	!
	93	! ATTENTION:
	94	! Physical quantities (like g, densities, etc.) used in this module still
	95	! have to be adjusted to those values used in the main PALM code.
	96	! Also, quantities in CGS-units should be converted to SI-units eventually.
[790]	97	!------------------------------------------------------------------------------!
	98
[1320]	99	USE constants, &
	100	ONLY: pi
	101
	102	USE kinds
	103
	104	USE particle_attributes, &
	105	ONLY: collision_kernel, dissipation_classes, particles, radius_classes
	106
[828]	107	USE pegrid
[790]	108
[828]	109
[790]	110	IMPLICIT NONE
	111
	112	PRIVATE
	113
[849]	114	PUBLIC ckernel, collision_efficiency_rogers, init_kernels, &
[1007]	115	rclass_lbound, rclass_ubound, recalculate_kernel
[790]	116
[1320]	117	REAL(wp) :: epsilon !:
	118	REAL(wp) :: eps2 !:
	119	REAL(wp) :: rclass_lbound !:
	120	REAL(wp) :: rclass_ubound !:
	121	REAL(wp) :: urms !:
	122	REAL(wp) :: urms2 !:
[790]	123
[1320]	124	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !:
	125	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !:
	126	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !:
	127
	128	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !:
	129	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !:
	130	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !:
	131	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !:
	132	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !:
	133
	134	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !:
[792]	135
[828]	136	SAVE
[792]	137
[790]	138	!
	139	!-- Public interfaces
[849]	140	INTERFACE collision_efficiency_rogers
	141	MODULE PROCEDURE collision_efficiency_rogers
	142	END INTERFACE collision_efficiency_rogers
	143
[828]	144	INTERFACE init_kernels
	145	MODULE PROCEDURE init_kernels
	146	END INTERFACE init_kernels
[790]	147
[828]	148	INTERFACE recalculate_kernel
	149	MODULE PROCEDURE recalculate_kernel
	150	END INTERFACE recalculate_kernel
[790]	151
	152
[828]	153	CONTAINS
[790]	154
[792]	155
[828]	156	SUBROUTINE init_kernels
	157	!------------------------------------------------------------------------------!
	158	! Initialization of the collision efficiency matrix with fixed radius and
	159	! dissipation classes, calculated at simulation start only.
	160	!------------------------------------------------------------------------------!
[792]	161
[828]	162	IMPLICIT NONE
[792]	163
[1320]	164	INTEGER(iwp) :: i !:
	165	INTEGER(iwp) :: j !:
	166	INTEGER(iwp) :: k !:
[790]	167
[828]	168
	169	!
	170	!-- Calculate collision efficiencies for fixed radius- and dissipation
	171	!-- classes
	172	IF ( collision_kernel(6:9) == 'fast' ) THEN
	173
	174	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	175	0:dissipation_classes), epsclass(1:dissipation_classes), &
	176	radclass(1:radius_classes) )
	177
	178	!
	179	!-- Calculate the radius class bounds with logarithmic distances
	180	!-- in the interval [1.0E-6, 2.0E-4] m
[1322]	181	rclass_lbound = LOG( 1.0E-6_wp )
	182	rclass_ubound = LOG( 2.0E-4_wp )
[1359]	183	radclass(1) = 1.0E-6_wp
[828]	184	DO i = 2, radius_classes
	185	radclass(i) = EXP( rclass_lbound + &
[1359]	186	( rclass_ubound - rclass_lbound ) * &
	187	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
[828]	188	ENDDO
	189
	190	!
[1007]	191	!-- Set the class bounds for dissipation in interval [0.0, 0.1] m2/s3
[828]	192	DO i = 1, dissipation_classes
[1359]	193	epsclass(i) = 0.1_wp * REAL( i, KIND=wp ) / dissipation_classes
[828]	194	ENDDO
	195	!
	196	!-- Calculate collision efficiencies of the Wang/ayala kernel
	197	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	198	ecf(1:radius_classes,1:radius_classes), &
	199	gck(1:radius_classes,1:radius_classes), &
	200	winf(1:radius_classes) )
	201
	202	DO k = 1, dissipation_classes
	203
	204	epsilon = epsclass(k)
[1359]	205	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	206
	207	CALL turbsd
	208	CALL turb_enhance_eff
	209	CALL effic
	210
	211	DO j = 1, radius_classes
	212	DO i = 1, radius_classes
	213	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	214	ENDDO
	215	ENDDO
	216
	217	ENDDO
	218
	219	!
	220	!-- Calculate collision efficiencies of the Hall kernel
	221	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	222	hwratio(1:radius_classes,1:radius_classes) )
	223
	224	CALL fallg
	225	CALL effic
	226
	227	DO j = 1, radius_classes
	228	DO i = 1, radius_classes
	229	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	230	* ec(i,j) * ABS( winf(j) - winf(i) )
	231	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	232	ENDDO
	233	ENDDO
	234
	235	!
	236	!-- Test output of efficiencies
	237	IF ( j == -1 ) THEN
	238
	239	PRINT, '** Hall kernel'
[1359]	240	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
[1007]	241	i = 1,radius_classes )
[828]	242	DO j = 1, radius_classes
[1007]	243	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	244	( hkernel(i,j), i = 1,radius_classes )
[828]	245	ENDDO
	246
	247	DO k = 1, dissipation_classes
	248	DO i = 1, radius_classes
	249	DO j = 1, radius_classes
[1359]	250	IF ( hkernel(i,j) == 0.0_wp ) THEN
	251	hwratio(i,j) = 9999999.9_wp
[828]	252	ELSE
	253	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	254	ENDIF
	255	ENDDO
	256	ENDDO
	257
	258	PRINT, '** epsilon = ', epsclass(k)
[1359]	259	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
[1007]	260	i = 1,radius_classes )
[828]	261	DO j = 1, radius_classes
[1359]	262	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
[1007]	263	( hwratio(i,j), i = 1,radius_classes )
[828]	264	ENDDO
	265	ENDDO
	266
	267	ENDIF
	268
	269	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	270
	271	ELSEIF( collision_kernel == 'hall' .OR. collision_kernel == 'wang' ) &
	272	THEN
	273	!
	274	!-- Initial settings for Hall- and Wang-Kernel
	275	!-- To be done: move here parts from turbsd, fallg, ecoll, etc.
	276	ENDIF
	277
	278	END SUBROUTINE init_kernels
	279
	280
[790]	281	!------------------------------------------------------------------------------!
[828]	282	! Calculation of collision kernels during each timestep and for each grid box
[790]	283	!------------------------------------------------------------------------------!
[828]	284	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	285
[1320]	286	USE arrays_3d, &
	287	ONLY: diss
[790]	288
[1320]	289	USE particle_attributes, &
[1359]	290	ONLY: prt_count, radius_classes, wang_kernel
[1320]	291
[790]	292	IMPLICIT NONE
	293
[1320]	294	INTEGER(iwp) :: i !:
	295	INTEGER(iwp) :: i1 !:
	296	INTEGER(iwp) :: j !:
	297	INTEGER(iwp) :: j1 !:
	298	INTEGER(iwp) :: k1 !:
	299	INTEGER(iwp) :: pend !:
	300	INTEGER(iwp) :: pstart !:
[790]	301
	302
[1359]	303	pstart = 1
	304	pend = prt_count(k1,j1,i1)
[828]	305	radius_classes = prt_count(k1,j1,i1)
[792]	306
[828]	307	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	308	radclass(1:radius_classes), winf(1:radius_classes) )
[790]	309
[828]	310	!
[1007]	311	!-- Store particle radii on the radclass array
	312	radclass(1:radius_classes) = particles(pstart:pend)%radius
[790]	313
[835]	314	IF ( wang_kernel ) THEN
[1007]	315	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
[835]	316	ELSE
[1359]	317	epsilon = 0.0_wp
[835]	318	ENDIF
[1359]	319	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
[790]	320
[1359]	321	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
[828]	322	!
	323	!-- Call routines to calculate efficiencies for the Wang kernel
	324	ALLOCATE( gck(1:radius_classes,1:radius_classes), &
	325	ecf(1:radius_classes,1:radius_classes) )
[790]	326
[828]	327	CALL turbsd
	328	CALL turb_enhance_eff
	329	CALL effic
[790]	330
[828]	331	DO j = 1, radius_classes
	332	DO i = 1, radius_classes
	333	ckernel(pstart+i-1,pstart+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
[790]	334	ENDDO
[828]	335	ENDDO
[790]	336
[828]	337	DEALLOCATE( gck, ecf )
[790]	338
	339	ELSE
[828]	340	!
	341	!-- Call routines to calculate efficiencies for the Hall kernel
[790]	342	CALL fallg
	343	CALL effic
	344
[828]	345	DO j = 1, radius_classes
	346	DO i = 1, radius_classes
	347	ckernel(pstart+i-1,pstart+j-1,1) = pi * &
	348	( radclass(j) + radclass(i) )**2 &
	349	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	350	ENDDO
	351	ENDDO
	352
	353	ENDIF
	354
[828]	355	DEALLOCATE( ec, radclass, winf )
[790]	356
[828]	357	END SUBROUTINE recalculate_kernel
[790]	358
[828]	359
[790]	360	!------------------------------------------------------------------------------!
[828]	361	! Calculation of gck
	362	! This is from Aayala 2008b, page 37ff.
	363	! Necessary input parameters: water density, radii of droplets, air density,
	364	! air viscosity, turbulent dissipation rate, taylor microscale reynolds number,
	365	! gravitational acceleration --> to be replaced by PALM parameters
[790]	366	!------------------------------------------------------------------------------!
[792]	367	SUBROUTINE turbsd
[799]	368
[1320]	369	USE control_parameters, &
	370	ONLY: g, molecular_viscosity
	371
	372	USE particle_attributes, &
	373	ONLY: radius_classes
[790]	374
	375	IMPLICIT NONE
[1320]	376
	377	LOGICAL, SAVE :: first = .TRUE. !:
[790]	378
[1320]	379	INTEGER(iwp) :: i !:
	380	INTEGER(iwp) :: j !:
[790]	381
[1320]	382	REAL(wp) :: ao !:
	383	REAL(wp) :: ao_gr !:
	384	REAL(wp) :: bbb !:
	385	REAL(wp) :: be !:
	386	REAL(wp) :: b1 !:
	387	REAL(wp) :: b2 !:
	388	REAL(wp) :: ccc !:
	389	REAL(wp) :: c1 !:
	390	REAL(wp) :: c1_gr !:
	391	REAL(wp) :: c2 !:
	392	REAL(wp) :: d1 !:
	393	REAL(wp) :: d2 !:
	394	REAL(wp) :: eta !:
	395	REAL(wp) :: e1 !:
	396	REAL(wp) :: e2 !:
	397	REAL(wp) :: fao_gr !:
	398	REAL(wp) :: fr !:
	399	REAL(wp) :: grfin !:
	400	REAL(wp) :: lambda !:
	401	REAL(wp) :: lambda_re !:
	402	REAL(wp) :: lf !:
	403	REAL(wp) :: rc !:
	404	REAL(wp) :: rrp !:
	405	REAL(wp) :: sst !:
	406	REAL(wp) :: tauk !:
	407	REAL(wp) :: tl !:
	408	REAL(wp) :: t2 !:
	409	REAL(wp) :: tt !:
	410	REAL(wp) :: t1 !:
	411	REAL(wp) :: vk !:
	412	REAL(wp) :: vrms1xy !:
	413	REAL(wp) :: vrms2xy !:
	414	REAL(wp) :: v1 !:
	415	REAL(wp) :: v1v2xy !:
	416	REAL(wp) :: v1xysq !:
	417	REAL(wp) :: v2 !:
	418	REAL(wp) :: v2xysq !:
	419	REAL(wp) :: wrfin !:
	420	REAL(wp) :: wrgrav2 !:
	421	REAL(wp) :: wrtur2xy !:
	422	REAL(wp) :: xx !:
	423	REAL(wp) :: yy !:
	424	REAL(wp) :: z !:
[790]	425
[1320]	426	REAL(wp), DIMENSION(1:radius_classes) :: st !:
	427	REAL(wp), DIMENSION(1:radius_classes) :: tau !:
	428
[799]	429	!
[828]	430	!-- Initial assignment of constants
[799]	431	IF ( first ) THEN
[790]	432
[799]	433	first = .FALSE.
[790]	434
[1007]	435	ENDIF
[790]	436
[1322]	437	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon ) ! in m
	438	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[828]	439	tl = urms**2 / epsilon ! in s
[1359]	440	lf = 0.5_wp * urms**3 / epsilon ! in m
[1007]	441	tauk = SQRT( molecular_viscosity / epsilon ) ! in s
[1322]	442	eta = ( molecular_viscosity3 / epsilon )0.25_wp ! in m
[1007]	443	vk = eta / tauk
[790]	444
[1359]	445	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
	446	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk ! in s
[799]	447
[1007]	448	CALL fallg ! gives winf in m/s
[790]	449
[828]	450	DO i = 1, radius_classes
[1007]	451	tau(i) = winf(i) / g ! in s
[828]	452	st(i) = tau(i) / tauk
[790]	453	ENDDO
	454
[828]	455	!
	456	!-- Calculate wr (from Aayala 2008b, page 38f)
	457	z = tt / tl
[1322]	458	be = SQRT( 2.0_wp ) * lambda / lf
[1359]	459	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
	460	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
	461	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp ! in m
	462	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
	463	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp ! in m
	464	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
	465	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
	466	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp ! in s
	467	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
	468	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp ! in s
[790]	469
[828]	470	DO i = 1, radius_classes
[790]	471
[1007]	472	v1 = winf(i) ! in m/s
[828]	473	t1 = tau(i) ! in s
[790]	474
[828]	475	DO j = 1, i
[1007]	476	rrp = radclass(i) + radclass(j)
	477	v2 = winf(j) ! in m/s
[828]	478	t2 = tau(j) ! in s
[790]	479
[1007]	480	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	481	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
	482	v1xysq = v1xysq * urms2 / t1 ! in m2/s**2
	483	vrms1xy = SQRT( v1xysq ) ! in m/s
[790]	484
[1007]	485	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	486	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
	487	v2xysq = v2xysq * urms2 / t2 ! in m2/s**2
	488	vrms2xy = SQRT( v2xysq ) ! in m/s
[790]	489
[828]	490	IF ( winf(i) >= winf(j) ) THEN
[799]	491	v1 = winf(i)
[790]	492	t1 = tau(i)
[799]	493	v2 = winf(j)
[790]	494	t2 = tau(j)
	495	ELSE
[799]	496	v1 = winf(j)
[790]	497	t1 = tau(j)
[799]	498	v2 = winf(i)
[790]	499	t2 = tau(i)
	500	ENDIF
	501
[828]	502	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	503	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	504	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	505	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	506	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1359]	507	v1v2xy = v1v2xy * fr * urms2 / tau(i) / tau(j) ! in m2/s**2
	508	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy ! in m2/s2
	509	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
[1322]	510	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
	511	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) ) ! in m/s
[790]	512
[828]	513	!
	514	!-- Calculate gr
	515	IF ( st(j) > st(i) ) THEN
	516	sst = st(j)
[790]	517	ELSE
[828]	518	sst = st(i)
[790]	519	ENDIF
	520
[1359]	521	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
	522	sst*2 + 5.3406_wp sst
	523	IF ( xx < 0.0_wp ) xx = 0.0_wp
	524	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
[790]	525
[1007]	526	c1_gr = xx / ( g / vk * tauk )**yy
[790]	527
[1322]	528	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[1359]	529	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
[828]	530	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta ! in cm
[790]	531
[1359]	532	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
	533	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
[790]	534
[1359]	535	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin ! in cm**3/s
[790]	536	gck(j,i) = gck(i,j)
	537
	538	ENDDO
	539	ENDDO
	540
[828]	541	END SUBROUTINE turbsd
[790]	542
[828]	543
[790]	544	!------------------------------------------------------------------------------!
[1007]	545	! phi_w as a function
[790]	546	!------------------------------------------------------------------------------!
[1320]	547	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[790]	548
	549	IMPLICIT NONE
	550
[1320]	551	REAL(wp) :: a !:
	552	REAL(wp) :: aa1 !:
	553	REAL(wp) :: b !:
	554	REAL(wp) :: tau0 !:
	555	REAL(wp) :: vsett !:
[790]	556
[1359]	557	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
	558	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2 ! in s
[790]	559
[1007]	560	END FUNCTION phi_w
[792]	561
[790]	562
	563	!------------------------------------------------------------------------------!
[1007]	564	! zhi as a function
[790]	565	!------------------------------------------------------------------------------!
[1320]	566	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[790]	567
	568	IMPLICIT NONE
	569
[1320]	570	REAL(wp) :: a !:
	571	REAL(wp) :: aa1 !:
	572	REAL(wp) :: aa2 !:
	573	REAL(wp) :: aa3 !:
	574	REAL(wp) :: aa4 !:
	575	REAL(wp) :: aa5 !:
	576	REAL(wp) :: aa6 !:
	577	REAL(wp) :: b !:
	578	REAL(wp) :: tau1 !:
	579	REAL(wp) :: tau2 !:
	580	REAL(wp) :: vsett1 !:
	581	REAL(wp) :: vsett2 !:
[790]	582
[1359]	583	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
	584	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
	585	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
	586	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
	587	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
	588	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
	589	vsett1 / vsett2
	590	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
	591	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
	592	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
	593	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3 ! in s**2
[799]	594
[828]	595	END FUNCTION zhi
[790]	596
[828]	597
[790]	598	!------------------------------------------------------------------------------!
[1007]	599	! Calculation of terminal velocity winf following Equations 10-138 to 10-145
	600	! from (Pruppacher and Klett, 1997)
[790]	601	!------------------------------------------------------------------------------!
[828]	602	SUBROUTINE fallg
[1320]	603
	604	USE cloud_parameters, &
	605	ONLY: rho_l
	606
	607	USE control_parameters, &
	608	ONLY: g
[790]	609
[1320]	610	USE particle_attributes, &
	611	ONLY: radius_classes
[790]	612
[1320]	613
[828]	614	IMPLICIT NONE
[790]	615
[1320]	616	INTEGER(iwp) :: i !:
	617	INTEGER(iwp) :: j !:
[790]	618
[1320]	619	LOGICAL, SAVE :: first = .TRUE. !:
[790]	620
[1320]	621	REAL(wp), SAVE :: cunh !:
	622	REAL(wp), SAVE :: eta !:
	623	REAL(wp), SAVE :: phy !:
	624	REAL(wp), SAVE :: py !:
	625	REAL(wp), SAVE :: rho_a !:
	626	REAL(wp), SAVE :: sigma !:
	627	REAL(wp), SAVE :: stb !:
	628	REAL(wp), SAVE :: stok !:
	629	REAL(wp), SAVE :: xlamb !:
[790]	630
[1320]	631	REAL(wp) :: bond !:
	632	REAL(wp) :: x !:
	633	REAL(wp) :: xrey !:
	634	REAL(wp) :: y !:
[799]	635
[1320]	636	REAL(wp), DIMENSION(1:7), SAVE :: b !:
	637	REAL(wp), DIMENSION(1:6), SAVE :: c !:
[799]	638
	639	!
[828]	640	!-- Initial assignment of constants
	641	IF ( first ) THEN
[799]	642
[828]	643	first = .FALSE.
[1359]	644	b = (/ -0.318657E1_wp, 0.992696E0_wp, -0.153193E-2_wp, &
	645	-0.987059E-3_wp, -0.578878E-3_wp, 0.855176E-4_wp, &
	646	-0.327815E-5_wp /)
	647	c = (/ -0.500015E1_wp, 0.523778E1_wp, -0.204914E1_wp, &
	648	0.475294E0_wp, -0.542819E-1_wp, 0.238449E-2_wp /)
[790]	649
[1007]	650	!
	651	!-- Parameter values for p = 1013,25 hPa and T = 293,15 K
[1359]	652	eta = 1.818E-5_wp ! in kg/(m s)
	653	xlamb = 6.6E-8_wp ! in m
	654	rho_a = 1.204_wp ! in kg/m**3
	655	cunh = 1.26_wp * xlamb ! in m
	656	sigma = 0.07363_wp ! in kg/s**2
	657	stok = 2.0_wp * g * ( rho_l - rho_a ) / ( 9.0_wp * eta ) ! in 1/(m s)
	658	stb = 32.0_wp * rho_a * ( rho_l - rho_a) * g / (3.0_wp * eta * eta)
[1007]	659	phy = sigma*3 rho_a2 / ( eta4 * g * ( rho_l - rho_a ) )
[1322]	660	py = phy**( 1.0_wp / 6.0_wp )
[790]	661
[828]	662	ENDIF
[790]	663
[828]	664	DO j = 1, radius_classes
[790]	665
[1359]	666	IF ( radclass(j) <= 1.0E-5_wp ) THEN
[799]	667
[1007]	668	winf(j) = stok * ( radclass(j)*2 + cunh radclass(j) )
[790]	669
[1359]	670	ELSEIF ( radclass(j) > 1.0E-5_wp .AND. radclass(j) <= 5.35E-4_wp ) THEN
[790]	671
[828]	672	x = LOG( stb * radclass(j)**3 )
[1359]	673	y = 0.0_wp
[790]	674
[828]	675	DO i = 1, 7
	676	y = y + b(i) * x**(i-1)
	677	ENDDO
[1007]	678	!
	679	!-- Note: this Eq. is wrong in (Pruppacher and Klett, 1997, p. 418)
	680	!-- for correct version see (Beard, 1976)
[1359]	681	xrey = ( 1.0_wp + cunh / radclass(j) ) * EXP( y )
[790]	682
[1359]	683	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
[790]	684
[1359]	685	ELSEIF ( radclass(j) > 5.35E-4_wp ) THEN
[790]	686
[1359]	687	IF ( radclass(j) > 0.0035_wp ) THEN
	688	bond = g * ( rho_l - rho_a ) * 0.0035_wp**2 / sigma
[828]	689	ELSE
[1007]	690	bond = g * ( rho_l - rho_a ) * radclass(j)**2 / sigma
[828]	691	ENDIF
[790]	692
[1359]	693	x = LOG( 16.0_wp * bond * py / 3.0_wp )
	694	y = 0.0_wp
[790]	695
[828]	696	DO i = 1, 6
	697	y = y + c(i) * x**(i-1)
	698	ENDDO
[790]	699
[828]	700	xrey = py * EXP( y )
[790]	701
[1359]	702	IF ( radclass(j) > 0.0035_wp ) THEN
	703	winf(j) = xrey * eta / ( 2.0_wp * rho_a * 0.0035_wp )
[828]	704	ELSE
[1359]	705	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
[828]	706	ENDIF
[790]	707
[828]	708	ENDIF
[790]	709
[828]	710	ENDDO
[790]	711
[828]	712	END SUBROUTINE fallg
[790]	713
[828]	714
[790]	715	!------------------------------------------------------------------------------!
[1071]	716	! Calculation of collision efficiencies for the Hall kernel
[790]	717	!------------------------------------------------------------------------------!
[828]	718	SUBROUTINE effic
[1320]	719
	720	USE particle_attributes, &
	721	ONLY: radius_classes
[790]	722
[828]	723	IMPLICIT NONE
[790]	724
[1320]	725	INTEGER(iwp) :: i !:
	726	INTEGER(iwp) :: iq !:
	727	INTEGER(iwp) :: ir !:
	728	INTEGER(iwp) :: j !:
	729	INTEGER(iwp) :: k !:
[790]	730
[1320]	731	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !:
[790]	732
[1320]	733	LOGICAL, SAVE :: first = .TRUE. !:
[790]	734
[1320]	735	REAL(wp) :: ek !:
	736	REAL(wp) :: particle_radius !:
	737	REAL(wp) :: pp !:
	738	REAL(wp) :: qq !:
	739	REAL(wp) :: rq !:
[790]	740
[1320]	741	REAL(wp), DIMENSION(1:21), SAVE :: rat !:
	742
	743	REAL(wp), DIMENSION(1:15), SAVE :: r0 !:
	744
	745	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !:
[790]	746
[792]	747	!
[828]	748	!-- Initial assignment of constants
	749	IF ( first ) THEN
[790]	750
[792]	751	first = .FALSE.
[1359]	752	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
	753	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
	754	150.0_wp, 200.0_wp, 300.0_wp /)
[790]	755
[1359]	756	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
	757	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
	758	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
	759	0.90_wp, 0.95_wp, 1.00_wp /)
	760
	761	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	762	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	763	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
	764	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
	765	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
	766	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
	767	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
	768	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
	769	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
	770	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
	771	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
	772	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
	773	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
	774	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
	775	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
	776	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
	777	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
	778	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	779	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
	780	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
	781	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	782	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
	783	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
	784	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	785	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
	786	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
	787	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	788	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
	789	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
	790	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	791	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
	792	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
	793	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	794	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
	795	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
	796	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	797	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
	798	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
	799	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	800	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
	801	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
	802	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	803	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
	804	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
	805	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	806	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
	807	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
	808	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	809	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
	810	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
	811	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	812	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
	813	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
	814	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
	815	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
	816	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
	817	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
	818	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
	819	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
	820	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
	821	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
	822	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
	823	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
[828]	824	ENDIF
[790]	825
[792]	826	!
[828]	827	!-- Calculate the radius class index of particles with respect to array r
[1007]	828	!-- Radius has to be in Âµm
[828]	829	ALLOCATE( ira(1:radius_classes) )
	830	DO j = 1, radius_classes
[1322]	831	particle_radius = radclass(j) * 1.0E6_wp
[828]	832	DO k = 1, 15
	833	IF ( particle_radius < r0(k) ) THEN
	834	ira(j) = k
	835	EXIT
	836	ENDIF
	837	ENDDO
	838	IF ( particle_radius >= r0(15) ) ira(j) = 16
	839	ENDDO
[790]	840
[792]	841	!
[828]	842	!-- Two-dimensional linear interpolation of the collision efficiency.
	843	!-- Radius has to be in Âµm
	844	DO j = 1, radius_classes
	845	DO i = 1, j
[792]	846
[828]	847	ir = ira(j)
	848	rq = radclass(i) / radclass(j)
	849	iq = INT( rq * 20 ) + 1
	850	iq = MAX( iq , 2)
[792]	851
[828]	852	IF ( ir < 16 ) THEN
	853	IF ( ir >= 2 ) THEN
[1322]	854	pp = ( ( radclass(j) * 1.0E06_wp ) - r0(ir-1) ) / &
[828]	855	( r0(ir) - r0(ir-1) )
[1359]	856	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	857	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
	858	* ecoll(ir-1,iq-1) &
	859	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
	860	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
[828]	861	+ pp * qq * ecoll(ir,iq)
	862	ELSE
	863	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	864	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
[828]	865	ENDIF
	866	ELSE
	867	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	868	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
[1346]	869	ec(j,i) = MIN( ek, 1.0_wp )
[1071]	870	ENDIF
[792]	871
[1359]	872	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
[1071]	873
[828]	874	ec(i,j) = ec(j,i)
[792]	875
[828]	876	ENDDO
	877	ENDDO
[792]	878
[828]	879	DEALLOCATE( ira )
[792]	880
[828]	881	END SUBROUTINE effic
[792]	882
	883
[790]	884	!------------------------------------------------------------------------------!
[828]	885	! Calculation of enhancement factor for collision efficencies due to turbulence
[790]	886	!------------------------------------------------------------------------------!
[828]	887	SUBROUTINE turb_enhance_eff
[790]	888
[1320]	889	USE particle_attributes, &
	890	ONLY: radius_classes
[790]	891
[828]	892	IMPLICIT NONE
[790]	893
[1320]	894	INTEGER(iwp) :: i !:
	895	INTEGER(iwp) :: iq !:
	896	INTEGER(iwp) :: ir !:
	897	INTEGER(iwp) :: j !:
	898	INTEGER(iwp) :: k !:
	899	INTEGER(iwp) :: kk !:
[790]	900
[1320]	901	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !:
	902
	903	LOGICAL, SAVE :: first = .TRUE. !:
[790]	904
[1320]	905	REAL(wp) :: particle_radius !:
	906	REAL(wp) :: pp !:
	907	REAL(wp) :: qq !:
	908	REAL(wp) :: rq !:
	909	REAL(wp) :: y1 !:
	910	REAL(wp) :: y2 !:
	911	REAL(wp) :: y3 !:
[790]	912
[1320]	913	REAL(wp), DIMENSION(1:11), SAVE :: rat !:
	914
	915	REAL(wp), DIMENSION(1:7), SAVE :: r0 !:
	916
	917	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !:
	918	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !:
[799]	919
	920	!
[828]	921	!-- Initial assignment of constants
	922	IF ( first ) THEN
[799]	923
[828]	924	first = .FALSE.
[799]	925
[1359]	926	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
	927	100.0_wp /)
	928
	929	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
	930	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
[828]	931	!
[1007]	932	!-- for 100 cm2/s3
[1359]	933	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
	934	1.207_wp, 1.207_wp, 1.0_wp /)
	935	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
	936	1.069_wp, 1.069_wp, 1.0_wp /)
	937	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
	938	1.000_wp, 1.000_wp, 1.0_wp /)
	939	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
	940	1.025_wp, 1.025_wp, 1.0_wp /)
	941	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
	942	1.056_wp, 1.056_wp, 1.0_wp /)
	943	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
	944	1.028_wp, 1.028_wp, 1.0_wp /)
	945	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
	946	1.046_wp, 1.046_wp, 1.0_wp /)
	947	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
	948	1.029_wp, 1.029_wp, 1.0_wp /)
	949	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
	950	1.021_wp, 1.021_wp, 1.0_wp /)
	951	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
	952	1.088_wp, 1.088_wp, 1.0_wp /)
	953	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
	954	2.60_wp, 2.60_wp, 1.0_wp /)
[828]	955	!
[1007]	956	!-- for 400 cm2/s3
[1359]	957	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
	958	1.445_wp, 1.445_wp, 1.0_wp /)
	959	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
	960	1.201_wp, 1.201_wp, 1.0_wp /)
	961	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
	962	1.150_wp, 1.150_wp, 1.0_wp /)
	963	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
	964	1.126_wp, 1.126_wp, 1.0_wp /)
	965	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
	966	1.092_wp, 1.092_wp, 1.0_wp /)
	967	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
	968	1.051_wp, 1.051_wp, 1.0_wp /)
	969	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
	970	1.086_wp, 1.086_wp, 1.0_wp /)
	971	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
	972	1.063_wp, 1.063_wp, 1.0_wp /)
	973	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
	974	1.100_wp, 1.100_wp, 1.0_wp /)
	975	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
	976	1.120_wp, 1.120_wp, 1.0_wp /)
	977	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
	978	26.0_wp, 26.0_wp, 1.0_wp /)
[799]	979
[828]	980	ENDIF
[790]	981
[828]	982	!
	983	!-- Calculate the radius class index of particles with respect to array r0
[1007]	984	!-- Radius has to be in Âµm
[828]	985	ALLOCATE( ira(1:radius_classes) )
[790]	986
[828]	987	DO j = 1, radius_classes
[1322]	988	particle_radius = radclass(j) * 1.0E6_wp
[828]	989	DO k = 1, 7
	990	IF ( particle_radius < r0(k) ) THEN
	991	ira(j) = k
	992	EXIT
	993	ENDIF
	994	ENDDO
	995	IF ( particle_radius >= r0(7) ) ira(j) = 8
	996	ENDDO
[799]	997
	998	!
[828]	999	!-- Two-dimensional linear interpolation of the collision efficiencies
[1007]	1000	!-- Radius has to be in Âµm
[828]	1001	DO j = 1, radius_classes
	1002	DO i = 1, j
[799]	1003
[828]	1004	ir = ira(j)
	1005	rq = radclass(i) / radclass(j)
[799]	1006
[828]	1007	DO kk = 2, 11
	1008	IF ( rq <= rat(kk) ) THEN
	1009	iq = kk
	1010	EXIT
	1011	ENDIF
	1012	ENDDO
[790]	1013
[1359]	1014	y1 = 0.0001_wp ! for 0 m2/s3
[1007]	1015
[828]	1016	IF ( ir < 8 ) THEN
	1017	IF ( ir >= 2 ) THEN
[1359]	1018	pp = ( radclass(j)*1.0E6_wp - r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[828]	1019	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	1020	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
	1021	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
	1022	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
	1023	pp * qq * ecoll_100(ir,iq)
	1024	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
	1025	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
	1026	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
	1027	pp * qq * ecoll_400(ir,iq)
[828]	1028	ELSE
	1029	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	1030	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	1031	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
[828]	1032	ENDIF
	1033	ELSE
	1034	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	1035	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	1036	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
[828]	1037	ENDIF
	1038	!
[1007]	1039	!-- Linear interpolation of dissipation rate in m2/s3
[1359]	1040	IF ( epsilon <= 0.01_wp ) THEN
	1041	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
	1042	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
	1043	ELSEIF ( epsilon <= 0.06_wp ) THEN
	1044	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	1045	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	1046	ELSE
[1359]	1047	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	1048	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	1049	ENDIF
[790]	1050
[1359]	1051	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
[790]	1052
[828]	1053	ecf(i,j) = ecf(j,i)
[790]	1054
[828]	1055	ENDDO
	1056	ENDDO
[790]	1057
[828]	1058	END SUBROUTINE turb_enhance_eff
[790]	1059
[849]	1060
	1061
	1062	SUBROUTINE collision_efficiency_rogers( mean_r, r, e)
	1063	!------------------------------------------------------------------------------!
	1064	! Collision efficiencies from table 8.2 in Rogers and Yau (1989, 3rd edition).
	1065	! Values are calculated from table by bilinear interpolation.
	1066	!------------------------------------------------------------------------------!
	1067
	1068	IMPLICIT NONE
	1069
[1320]	1070	INTEGER(iwp) :: i !:
	1071	INTEGER(iwp) :: j !:
	1072	INTEGER(iwp) :: k !:
[849]	1073
[1320]	1074	LOGICAL, SAVE :: first = .TRUE. !:
[849]	1075
[1320]	1076	REAL(wp) :: aa !:
	1077	REAL(wp) :: bb !:
	1078	REAL(wp) :: cc !:
	1079	REAL(wp) :: dd !:
	1080	REAL(wp) :: dx !:
	1081	REAL(wp) :: dy !:
	1082	REAL(wp) :: e !:
	1083	REAL(wp) :: gg !:
	1084	REAL(wp) :: mean_r !:
	1085	REAL(wp) :: mean_rm !:
	1086	REAL(wp) :: r !:
	1087	REAL(wp) :: rm !:
	1088	REAL(wp) :: x !:
	1089	REAL(wp) :: y !:
	1090
[1359]	1091	REAL(wp), DIMENSION(1:9), SAVE :: collected_r = 0.0_wp !:
[1320]	1092
[1359]	1093	REAL(wp), DIMENSION(1:19), SAVE :: collector_r = 0.0_wp !:
[1320]	1094
[1359]	1095	REAL(wp), DIMENSION(1:9,1:19), SAVE :: ef = 0.0_wp !:
[849]	1096
[1322]	1097	mean_rm = mean_r * 1.0E06_wp
	1098	rm = r * 1.0E06_wp
[849]	1099
	1100	IF ( first ) THEN
	1101
[1359]	1102	collected_r = (/ 2.0_wp, 3.0_wp, 4.0_wp, 6.0_wp, 8.0_wp, &
	1103	10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp /)
	1104	collector_r = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, &
	1105	60.0_wp, 80.0_wp, 100.0_wp, 150.0_wp, 200.0_wp, &
	1106	300.0_wp, 400.0_wp, 500.0_wp, 600.0_wp, 1000.0_wp, &
	1107	1400.0_wp, 1800.0_wp, 2400.0_wp, 3000.0_wp /)
[849]	1108
[1359]	1109	ef(:,1) = (/ 0.017_wp, 0.027_wp, 0.037_wp, 0.052_wp, 0.052_wp, &
	1110	0.052_wp, 0.052_wp, 0.0_wp, 0.0_wp /)
	1111	ef(:,2) = (/ 0.001_wp, 0.016_wp, 0.027_wp, 0.060_wp, 0.12_wp, &
	1112	0.17_wp, 0.17_wp, 0.17_wp, 0.0_wp /)
	1113	ef(:,3) = (/ 0.001_wp, 0.001_wp, 0.02_wp, 0.13_wp, 0.28_wp, &
	1114	0.37_wp, 0.54_wp, 0.55_wp, 0.47_wp/)
	1115	ef(:,4) = (/ 0.001_wp, 0.001_wp, 0.02_wp, 0.23_wp, 0.4_wp, &
	1116	0.55_wp, 0.7_wp, 0.75_wp, 0.75_wp/)
	1117	ef(:,5) = (/ 0.01_wp, 0.01_wp, 0.03_wp, 0.3_wp, 0.4_wp, &
	1118	0.58_wp, 0.73_wp, 0.75_wp, 0.79_wp/)
	1119	ef(:,6) = (/ 0.01_wp, 0.01_wp, 0.13_wp, 0.38_wp, 0.57_wp, &
	1120	0.68_wp, 0.80_wp, 0.86_wp, 0.91_wp/)
	1121	ef(:,7) = (/ 0.01_wp, 0.085_wp, 0.23_wp, 0.52_wp, 0.68_wp, &
	1122	0.76_wp, 0.86_wp, 0.92_wp, 0.95_wp/)
	1123	ef(:,8) = (/ 0.01_wp, 0.14_wp, 0.32_wp, 0.60_wp, 0.73_wp, &
	1124	0.81_wp, 0.90_wp, 0.94_wp, 0.96_wp/)
	1125	ef(:,9) = (/ 0.025_wp, 0.25_wp, 0.43_wp, 0.66_wp, 0.78_wp, &
	1126	0.83_wp, 0.92_wp, 0.95_wp, 0.96_wp/)
	1127	ef(:,10) = (/ 0.039_wp, 0.3_wp, 0.46_wp, 0.69_wp, 0.81_wp, &
	1128	0.87_wp, 0.93_wp, 0.95_wp, 0.96_wp/)
	1129	ef(:,11) = (/ 0.095_wp, 0.33_wp, 0.51_wp, 0.72_wp, 0.82_wp, &
	1130	0.87_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
	1131	ef(:,12) = (/ 0.098_wp, 0.36_wp, 0.51_wp, 0.73_wp, 0.83_wp, &
	1132	0.88_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
	1133	ef(:,13) = (/ 0.1_wp, 0.36_wp, 0.52_wp, 0.74_wp, 0.83_wp, &
	1134	0.88_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
	1135	ef(:,14) = (/ 0.17_wp, 0.4_wp, 0.54_wp, 0.72_wp, 0.83_wp, &
	1136	0.88_wp, 0.94_wp, 0.98_wp, 1.0_wp /)
	1137	ef(:,15) = (/ 0.15_wp, 0.37_wp, 0.52_wp, 0.74_wp, 0.82_wp, &
	1138	0.88_wp, 0.94_wp, 0.98_wp, 1.0_wp /)
	1139	ef(:,16) = (/ 0.11_wp, 0.34_wp, 0.49_wp, 0.71_wp, 0.83_wp, &
	1140	0.88_wp, 0.94_wp, 0.95_wp, 1.0_wp /)
	1141	ef(:,17) = (/ 0.08_wp, 0.29_wp, 0.45_wp, 0.68_wp, 0.8_wp, &
	1142	0.86_wp, 0.96_wp, 0.94_wp, 1.0_wp /)
	1143	ef(:,18) = (/ 0.04_wp, 0.22_wp, 0.39_wp, 0.62_wp, 0.75_wp, &
	1144	0.83_wp, 0.92_wp, 0.96_wp, 1.0_wp /)
	1145	ef(:,19) = (/ 0.02_wp, 0.16_wp, 0.33_wp, 0.55_wp, 0.71_wp, &
	1146	0.81_wp, 0.90_wp, 0.94_wp, 1.0_wp /)
[849]	1147
	1148	ENDIF
	1149
	1150	DO k = 1, 8
	1151	IF ( collected_r(k) <= mean_rm ) i = k
	1152	ENDDO
	1153
	1154	DO k = 1, 18
	1155	IF ( collector_r(k) <= rm ) j = k
	1156	ENDDO
	1157
[1359]	1158	IF ( rm < 10.0_wp ) THEN
	1159	e = 0.0_wp
	1160	ELSEIF ( mean_rm < 2.0_wp ) THEN
	1161	e = 0.001_wp
	1162	ELSEIF ( mean_rm >= 25.0_wp ) THEN
	1163	IF( j <= 2 ) e = 0.0_wp
	1164	IF( j == 3 ) e = 0.47_wp
	1165	IF( j == 4 ) e = 0.8_wp
	1166	IF( j == 5 ) e = 0.9_wp
	1167	IF( j >=6 ) e = 1.0_wp
	1168	ELSEIF ( rm >= 3000.0_wp ) THEN
	1169	IF( i == 1 ) e = 0.02_wp
	1170	IF( i == 2 ) e = 0.16_wp
	1171	IF( i == 3 ) e = 0.33_wp
	1172	IF( i == 4 ) e = 0.55_wp
	1173	IF( i == 5 ) e = 0.71_wp
	1174	IF( i == 6 ) e = 0.81_wp
	1175	IF( i == 7 ) e = 0.90_wp
	1176	IF( i >= 8 ) e = 0.94_wp
[849]	1177	ELSE
	1178	x = mean_rm - collected_r(i)
	1179	y = rm - collector_r(j)
	1180	dx = collected_r(i+1) - collected_r(i)
	1181	dy = collector_r(j+1) - collector_r(j)
	1182	aa = x2 + y2
	1183	bb = ( dx - x )2 + y2
	1184	cc = x2 + ( dy - y )2
	1185	dd = ( dx - x )2 + ( dy - y )2
	1186	gg = aa + bb + cc + dd
	1187
	1188	e = ( (gg-aa)ef(i,j) + (gg-bb)ef(i+1,j) + (gg-cc)*ef(i,j+1) + &
[1359]	1189	(gg-dd)ef(i+1,j+1) ) / (3.0_wp gg)
[849]	1190	ENDIF
	1191
	1192	END SUBROUTINE collision_efficiency_rogers
	1193
[825]	1194	END MODULE lpm_collision_kernels_mod

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